This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365573 #6 Sep 27 2023 13:43:32 %S A365573 0,0,0,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,1,0,0,1,1,1,1,1,0,1,0,1,0, %T A365573 1,0,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0, %U A365573 1,1,0,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,0,2,2,1,0,0,1,0,1 %N A365573 Number of primes between prime(n) and prime(n)+log(prime(n)), exclusive. %C A365573 Inspired by A354841. %F A365573 Conjecture: Limit_{N->oo} (Ratio_{n=1..N} a(n)=0) = 1/e (A068985). %o A365573 (PARI) a(n) = primepi(prime(n)+log(prime(n))) - primepi(prime(n)) %Y A365573 Cf. A068985, A354841, A275235. %K A365573 nonn %O A365573 1,88 %A A365573 _Alain Rocchelli_, Sep 09 2023